[Xanthul]

250 its not 2/n. Its not picking 2 doors between N doors, its picking a door from N doors, then leaving only 2 doors, and choosing between them. Read the problem carefully, its not the same.

For example, with 100 doors: The host knows that prize is in door number 55, for example. So now, you pick a door randomly, for example #34. Then the host opens all doors except door #55 because HE KNOWS that the prize is there and he cant show it. He has to leave only 2 doors closed: one is your pick, and the other one most of the times will be the prized one (unless you picked the prized one in your first choice, in which case he will have to choose a door randomly).

Now, the discussion is whether door 34 and 55 have 50% chances each, or if door 34 has only 1% chance and door 55 has 99% chance. Im sure its the second one, because 99% of the times you will have MISSED your first choice (even if you still DONT KNOW IT), and the host will have to leave closed the prized door, therefore POINTING you which one is the prized one.

With N doors, if you ALWAYS change your first choice, you will win the prize with a probability of N-1/N.